How to Calculate Maximum Torque Angle

Written by brendan conuel
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How to Calculate Maximum Torque Angle
You apply torque to a twist-off bottle cap in order to open the bottle. (Twist image by irum from

Torque is a measure of the degree to which an influence acting on a body will induce rotation. It can be thought of as the rotational expression of force. Torque comes about as a result of a force being applied to a specific location on a body capable of rotation, such as a lever about a pivot or a globe about a central axis. The strength of a torque is dependent on the angle at which the torque-inducing force is applied. Knowing the correct angle to maximise the torque produced from a given force can prove useful in a variety of engineering and construction applications.

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Things you need

  • Trigonometric calculator

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  1. 1

    Consider the symbolic definition of torque: T = r x F x sin(theta). Here, T represents torque, r represents the distance separating the axis of rotation from where the force is applied, F represents the force, and theta represents the angle at which the force is applied.

  2. 2

    To calculate the maximum torque angle, you need to know what value of theta will produce the largest possible value of T for a given force. Since the distance r and the force F are not dependent on theta, you can treat them as constants and essentially ignore them.

  3. 3

    Determine what value of theta will produce the largest possible value of sin(theta) as this will in turn produce the largest possible value of T.

  4. 4

    Recall that the maximum value of the function sin(theta) is 1.

  5. 5

    Determine what angle lends itself to a sine function of value 1. This is called determining the inverse sine of a number. To express this question in a calculator, press the sin^-1, then by 1.

    You will get 90 degrees. Applying a force at a 90 degree angle produces the maximum possible torque for that force at that location.

Tips and warnings

  • If your calculator is in radians mode, you will get Pi/2 (approximately 1.571) radians instead of 90 degrees. The expressions are equivalent.
  • Torque is a vector quantity. When expressing it, always remember to include direction.

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